Probabilidad y estadística from edX

La Probabilidad es la rama de las matemáticas que estudia la incertidumbre. Entre otras cosas, busca desarrollar herramientas matemáticas que ayuden al ser humano a analizar y a tomar decisiones frente a situaciones inciertas. De igual manera, la estadística es una disciplina que utiliza teoría de probabilidad para adquirir, organizar y analizar datos, de tal forma que, utilizando la información "escondida" en ellos, se pueda cuantificar y manejar la incertidumbre asociada a un determinado escenario de la vida real.

Este curso busca ser un primer encuentro con la teoría de la probabilidad y con algunas de las aplicaciones más frecuentes y sencillas de esta teoría en el área de la estadística.

El curso está orientado a estudiantes de primer o segundo año de ingeniería, economía, matemáticas u otras ciencias básicas. Sin embargo, estudiantes o profesionales de éstas y otras áreas estarán perfectamente capacitados para tomarlo siempre y cuando tengan conocimientos básicos en cálculo y en matemáticas (particularmente en cómo realizar demostraciones y en algunos objetos matemáticos elementales como por ejemplo, las funciones o los conjuntos de números más frecuentes).

Se abordan conceptos introductorios pero a la vez esenciales en Probabilidad y en Estadística, como bases en Teoría de probabilidad, sin profundizar demasiado en conceptos avanzados de matemáticas pero manteniendo el rigor necesario para garantizar una comprensión intuitiva y adecuada de ellas.

Dicho de otra forma, este curso trata de ser lo más estricto y preciso posible evitando utilizar conceptos muy complejos que serían necesarios para introducir la teoría completamente. Más aún, se acompañará la teoría con aplicaciones prácticas en contextos que involucren situaciones inciertas en las que se utilizan los conceptos antes presentados.

Las bases teóricas introducidas en el curso representan los pilares sobre los cuales se construyen diversas metodologías indispensables en la estadística y en la ciencia de datos, muchas de las cuales serán también cubiertas en las fases más avanzadas de él.

What's inside

Learning objectives

Conocer las bases teóricas de la probabilidad, modelos probabilísticos, funciones y axiomas de probabilidad e identificar aplicaciones de conteo en escenarios frecuentes que presentan algún grado de incertidumbre.
Reconocer la teoría y las aplicaciones de las variables aleatorias (discretas y continuas), y generalizar los conceptos previamente vistos al contexto de múltiples variables aleatorias conjuntas.
Comprender los teoremas de límite probabilísticos fundamentales de la estadística moderna.

Identificar desde el enfoque de la estadística, la estimación paramétrica y las pruebas de hipótesis.
Elaborar modelos probabilísticos en la forma de regresiones lineales.

Conocer las bases teóricas de la probabilidad, modelos probabilísticos, funciones y axiomas de probabilidad e identificar aplicaciones de conteo en escenarios frecuentes que presentan algún grado de incertidumbre.
Reconocer la teoría y las aplicaciones de las variables aleatorias (discretas y continuas), y generalizar los conceptos previamente vistos al contexto de múltiples variables aleatorias conjuntas.
Comprender los teoremas de límite probabilísticos fundamentales de la estadística moderna.
Identificar desde el enfoque de la estadística, la estimación paramétrica y las pruebas de hipótesis.
Elaborar modelos probabilísticos en la forma de regresiones lineales.

Syllabus

Sección 1. Eventos y conteo

* Introducción a teoría de conjuntos y modelo probabilístico

* Probabilidad

* Independencia entre eventos y herramientas de conteo

Sección 2. Variables aleatorias discretas y continuas

* Introducción

* Valor esperado, momentos, varianza

* Variables aleatorias discretas

* Variables aleatorias continuas

* Múltiples variables aleatorias

* Más sobre variables aleatorias

Sección 3. Desigualdades y teoremas límite

* Desigualdades

* Teoremas límite

Sección 4. Métodos de estimación y pruebas de hipótesis

* Estimadores

* Intervalos y Método

* Pruebas de hipótesis

Sección 5. Modelos lineales

* Modelos probabilísticos

* Mínimos cuadrados

Pruebas de hipótesis

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Esta dirigido a estudiantes de primer o segundo año de estas disciplinas

Los estudiantes y profesionales de estas y otras áreas que posean conocimientos básicos en cálculo y matemáticas pueden tomar el curso

Aborda conceptos esenciales de probabilidad y estadística

Proporciona una base adecuada para metodologías avanzadas en estadística y ciencia de datos

El rigor matemático garantiza una comprensión adecuada

Utiliza ejemplos prácticos para ilustrar los conceptos

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Probabilidad y estadística with these activities:

Organize Course Notes and Supplementary Materials

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Stay organized by compiling course notes, assignments, and other materials to facilitate effective review and knowledge retention.

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Create a dedicated folder or notebook for course materials
Sort and label materials by topic or module
Review and annotate materials regularly to reinforce learning

Explore Probability Theory on Khan Academy

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Engage in guided tutorials on Khan Academy to supplement your understanding of probability theory.

Browse courses on Probability Theory

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Watch videos on basic probability concepts
Complete practice exercises to reinforce your knowledge

Create Probability Simulation Projects

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Design and execute probability simulation projects to visualize and understand probability concepts in practice.

Browse courses on Monte Carlo simulations

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Define the simulation scenario and objectives
Develop a simulation model using a programming language or spreadsheet
Run simulations and collect data
Analyze and interpret simulation results

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Career center

Learners who complete Probabilidad y estadística will develop knowledge and skills that may be useful to these careers:

Statistician

Statisticians collect, analyze, and interpret data. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to design and conduct statistical studies, collect and analyze data, and draw meaningful conclusions. This knowledge will help you build the skills necessary to succeed as a Statistician.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to develop and implement quantitative models, and how to use them to make informed investment decisions. This knowledge will help you build the skills necessary to succeed as a Quantitative Analyst.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve problems in business and industry. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to model and analyze complex systems, and how to develop and implement solutions to real-world problems. This knowledge will help you build the skills necessary to succeed as an Operations Research Analyst.

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Data Scientist

Data Scientists use data to solve business problems and make informed decisions. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to collect, clean, and analyze data, and how to use statistical methods to draw meaningful conclusions. This knowledge will help you build the skills necessary to succeed as a Data Scientist.

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Data Analyst

Data Analysts use data to solve business problems and make informed decisions. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to collect, clean, and analyze data, and how to use statistical methods to draw meaningful conclusions. This knowledge will help you build the skills necessary to succeed as a Data Analyst.

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Risk Manager

Risk Managers identify and assess risks, and develop and implement strategies to mitigate those risks. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to identify and assess risks, and how to develop and implement effective risk management strategies. This knowledge will help you build the skills necessary to succeed as a Risk Manager.

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Machine Learning Engineer

Machine Learning Engineers develop and implement machine learning models. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to develop and implement machine learning models, and how to use them to solve real-world problems. This knowledge will help you build the skills necessary to succeed as a Machine Learning Engineer.

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Actuary

Actuaries analyze the financial implications of uncertain future events, using mathematical and statistical techniques to assess risk. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to calculate probabilities, model random variables, and apply statistical methods to real-world problems. This knowledge will help you build the skills necessary to succeed as an Actuary.

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Market Researcher

Market Researchers use research methods to gather and analyze data about markets and customers. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to design and conduct research studies, collect and analyze data, and draw meaningful conclusions. This knowledge will help you build the skills necessary to succeed as a Market Researcher.

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Business Analyst

Business Analysts use data to solve business problems and make informed decisions. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to collect, clean, and analyze data, and how to use statistical methods to draw meaningful conclusions. This knowledge will help you build the skills necessary to succeed as a Business Analyst.

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Financial Analyst

Financial Analysts use financial data to make investment recommendations. This course provides a strong foundation in probability and statistics, which are essential for success in this field. You will learn how to analyze financial data, identify trends, and make predictions. This knowledge will help you build the skills necessary to succeed as a Financial Analyst.

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Financial Manager

Financial Managers are responsible for the financial health of organizations. This course may be useful for Financial Managers who want to build a foundation in probability and statistics. You will learn how to use probability and statistics to model and analyze financial data, and how to use this knowledge to make better decisions about financial management.

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Software Engineer

Software Engineers design, develop, and implement software systems. This course may be useful for Software Engineers who want to build a foundation in probability and statistics. You will learn how to use probability and statistics to model and analyze complex systems, and how to use this knowledge to develop more effective software systems.

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Product Manager

Product Managers are responsible for the development and marketing of products. This course may be useful for Product Managers who want to build a foundation in probability and statistics. You will learn how to use probability and statistics to model and analyze product demand, and how to use this knowledge to make better decisions about product development and marketing.

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Marketing Manager

Marketing Managers are responsible for the development and implementation of marketing campaigns. This course may be useful for Marketing Managers who want to build a foundation in probability and statistics. You will learn how to use probability and statistics to model and analyze consumer behavior, and how to use this knowledge to develop more effective marketing campaigns.

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